Analytical calculation of the torque exerted between two perpendicularly magnetized magnets

Analytical expressions of the torque on cuboidal permanent magnets are given. The only hypothesis is that the magnetizations are rigid, uniform, and perpendicularly oriented. The analytical calculation is made by replacing magnetizations by distributions of magnetic charges on the magnet poles. The torque expressions are obtained using the Lorentz force method. The results are valid for any relative magnet position, and the torque can be obtained with respect to any reference point. Although these expressions seem rather complicated, they enable an extremely fast and accurate torque calculation on a permanent magnet in the presence of a magnetic field of another permanent magnet.